A155203 G.f.: A(x) = exp( Sum_{n>=1} 3^(n^2) * x^n/n ), a power series in x with integer coefficients.

1, 3, 45, 6687, 10782369, 169490304819, 25016281429306077, 34185693516532070487615, 429210580094546346191627404353, 49269611092414945570325157106493868771

Offset: 0

Author

Paul D. Hanna, Feb 04 2009

Keywords

• nonn

Comments

More generally, for m integer, exp( Sum_{n>=1} m^(n^2) * x^n/n ) is a power series in x with integer coefficients.

Examples

			G.f.: A(x) = 1 + 3*x + 45*x^2 + 6687*x^3 + 10782369*x^4 + 169490304819*x^5 +...
log(A(x)) = 3*x + 3^4*x^2/2 + 3^9*x^3/3 + 3^16*x^4/4 + 3^25*x^5/5 +...
		

Crossrefs

Cf. A060722, A155204, A155205, A155206, A155812 (triangle), variants: A155200, A155207.

Programs

PARI

{a(n)=polcoeff(exp(sum(m=1,n+1,3^(m^2)*x^m/m)+x*O(x^n)),n)}

Formula

Equals column 0 of triangle A155812.

G.f. satisfies: A'(x)/A(x) = 3 + 27*x*A'(9*x)/A(9*x). - Paul D. Hanna, Nov 15 2022

a(n) ~ 3^(n^2)/n. - Vaclav Kotesovec, Oct 31 2024